Authority is both the central power that law and its institutions claim to wield and is seemingly central to the very idea of legality. Many legal theorists have argued that one of the features of legality is a claim to legitimate authority – that law, unlike other normative systems, claims to have legitimate authority that is both comprehensive and supreme. International law, however, seems to make a different kind of claim, which cannot plausibly be interpreted as a claim to independently legitimate authority, and, thus, creates a gap that threatens to disrupt the analytical nexus between authority and legality. This article argues that international law’s claims to authority, embodied within its institutions, regimes and specific rules, should instead be understood as claims to relative, interdependent authority. It then argues that under a conventional understanding of independent authority there would be a second, normative gap between the claim to legitimate authority made by international institutions and the extent of the legitimate authority they possess. To bridge this normative gap, the article argues again for the relativity of legitimate authority, in which the existence of legitimate authority in international law depends upon the relationships its institutions have with states and other authorities with which they interact.